Question

Find the roots of the equation $x^2–18x+12=0$ by the method of completing the square.

• A. $x=9\pm \sqrt{6}$
• B. $x=6\pm \sqrt{62}$
• C. $x=6\pm \sqrt{69}$
• D. $x=9\pm \sqrt{69}$

Answer 1

The correct option is D $x=9\pm \sqrt{69}$

Given: $x^2–18x+12=0$
This is same as:
$x^2–18x=-12$

Adding the square of one-half of the coefficient of x [i.e., $(\frac{1}{2}\times -18{)}^2$] to both sides,

$x^2–[2\times (x)\times 9]+(-9{)}^2=(-9{)}^2-12$
$\Rightarrow x^2–[2\times (x)\times 9]+(9{)}^2=81-12$
$\Rightarrow (x–9{)}^2=69$
$\Rightarrow x-9=\pm \sqrt{69}$
$\Rightarrow x=9\pm \sqrt{69}$